Death Saves and Survival Rates

In 4th Edition Dungeons & Dragons, if your character's hit points enter
the range between zero and negative half of their maximum hit points, they are
dying. Each round at the end of their turn, they roll a saving throw. On a 1
to 9, the character accumulates a failure. On their third failure the
character dies. On a 10 to 19, nothing happens, the character remains dying.
On a 20 or better, if the character has a healing surge, they can spend it and
cease to be dying.

Notes

Probabilities were calculated exactly. This was done by exhaustive examination of all possible results with results tracked in fractional form. They were then converted to percentages, as 27.09% is easier to read than 56829003/209715200.

There are multiple tables. In each I vary the save modifier and how many previous death saves the character has failed. The only save modifier I'm currently aware of is from the feat "Human Perseverance", which grants a modifier of +1.

All probabilities are cumulative. So assuming no modifiers or previous failures, after 10 rounds a character with -1 hit points will have a 26% chance of having rolled a 20 and gotten back up within those 10 rounds, and a 69% chance of having died somewhere during rounds 3 through 10.

In all cases, it's assumed that the character has at least one healing surge left. If a character didn't have a healing surge, the "Surge" column would be unevenly split between "OK" and "Dead."

The headers mean the following:

Surge means "Rolled a 20 or better on this or an previous round, spent a healing surge, and no longer is dying."Okay means "Not yet dead, but may yet."Dead means "Died on this or a previous round."No failures is included in the "Okay" results. It means that the character has failed 0 death saving throws.1 failure is included in the "Okay" results. It means that the character has failed 1 death saving throw.2 failures is included in the "Okay" results. It means that the character has failed 2 death saving throws.
There is no "3 failures", since that is just "Dead."

Due to rounding, numbers may not add up to 100%. Also, due to rounding "0.00%" typically means "less than 0.01%", not 0.

I've tried to generate numbers for the most common cases. If anyone is interested in other tables, or for tables with the fractions, get in touch!